The Irish Republican Army has had numerous different incarnations, and many disparate groupings have laid claim to the name. The organisation generally known as the IRA today is the Provisional IRA, a result of a split which happened in the 1970s, shortly after the beginning of the current conflict in Northern Ireland.
The original IRA, now often termed the Old IRA, was the organisation which fought the British in the Irish War of Independence. It was formed from various groups such as the Irish Republican Brotherhood, the Irish Citizens Army and the Irish Volunteers (the Irish Language name of the IRA, Óglaigh na hÉireann, translates as the Irish Volunteers). Led by Micheal Collins, they fought a guerrilla war, although they are often termed the founders of modern terrorism. They succeeding in permanently destabilising British rule in Ireland, although the majority of those in six counties of what is now known as Northern Ireland wished to remain within the United Kingdom.
In 1922, most of the members of the IRA participated in the founding of the Irish Free State, forming this entity's regular army. However, more dogmatic republicans rejected the state, as it was not a full republic and retained links with the British crown. These dissidents retained the title IRA, and fought a bloody and ultimately pointless civil war against the new state.
These "irregulars" were unsuccessful, and most eventually reconciled themselves to participation in the new state, although they retained their republican aspirations. They formed the Fianna Fáil party, which, although it continues to term itself "The Republican Party", has rejected all violent means and transformed itself into a national political movement.
The IRA of the civil war never disbanded, however, and a rump fought for many years various low-key campaigns against partition. Its level of activity, however, was very low compared to the conflicts which had passed, and those which were to come. Eventually its main leadership drifted away from dogmatic republicanism into radical socialism. Again, many adherents found their way into constitutional politics.
In 1968, however, the Civil Rights movement in the North sparked off new conflict. Catholics marched in support of claims for equal treatment in issues such as housing, and an end to widespread gerrymandering. Dormant republicanism was awoken by attacks on Catholic homes, with hundreds of families being burnt out. Those in the Civil Rights movement called for non-violent methods, after the model of Martin Luther King. However, the armed IRA sprung up again to take on the British, whom they saw as an occupying force.
At this point, a disagreement over tactics and ideology led the IRA to split into the Official IRA and the Provisional IRA. By far the more militant group, the Provisionals attracted many members in the North and elsewhere in Ireland after atrocities such as Bloody Sunday in 1972, when Civil Rights marchers where fired on by British soldiers.
The campaign which the Provos subsequently waged was unprecedented in terms of its ruthlessness, ferocity and sheer horror. Although loyalist organisations such as the UVF and UFF engaged them and adopted their terrorist tactics, no organisation has been responsible for more of the over 3000 deaths in the current conflict than the Provisional IRA. Their absolute ferocity quickly alienated them from the vast majority of Irish people, even those of republican leanings. They commanded greater support within Northern Ireland, although they also terrorised their own communities through punishment beatings, kneecappings and assassinations. The mainstream of Irish nationalism in Northern Ireland was represented not by the IRA's political wing Sinn Féin, but by the constitutional SDLP.
In 1994 the Provos called a ceasefire, and although they subsequently broke this, another was called in 1997, which lasts to the present day. All-party peace negotiations are underway, but are inconclusive at the time of writing. The Provos have apparently accepted that their campaign is unwinnable, but they have as yet refused to declare that their war is over.
Since the Provos' ceasefire in 1997, other groupings, involving dissident Provos, have attempted to appropriate the name IRA, such as the so-called "Real IRA" (formed by Provos who broke away in 1997), and the Continuity IRA (an organisation which dates back to the split of 1986).